Digits in a measurement that are important for it are called significant figures (or significant digits). Using them keeps us honest, because we are prevented from seeming overly precise in our work.
In order to present results with the proper precision, we need to know how many significant figures are present in each number we use in a calculation. There are four basic rules:
- Zeroes in the beginning of a number never count.
- Zeroes at the end of a number count only if there is a written decimal point.
- The digits 1 - 9 always count.
- Zeroes between the digits 1 - 9 always count.
(the answers are 1, 2, 2, 2, 3, 3, 5, 2, 3).
When adding or subtracting, the answer can only be as precise as the least precise number used. For example, a 250 pound person who has a hair pulled out (say, 0.001 pounds) still weighs 250 pounds. That's because the last significant digit is the 5 (in the tens place), and everything after that is not even estimated. So you have no idea how many ones of pounds the guy weighs, or how many tenths, or hundredths, or thousandths. Therefore, you have no idea what from to subtract 0.001 pounds. So he still weighs 250 pounds.
When multiplying or dividing, the answer has the same number of significant digits as the number used with the least. For instance, there is a quick estimation of pi (p) as 22¸7. On a calculator, that gives 3.1428571423, which is pretty close. But if you had measured a circle as 22 feet around and 7 feet across, the answer must be rounded to "3" to match the least number of significant digits.
*remember*
when multiplying/dividing, round it to the fewest number significant digits.
VIDEOS! :) .. on significant figures
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